This paper presents a study of the Wound Rotor Synchronous Machine (SM) stability undervoltage sags (dips). Machine behavior has been analyzed by considering different magnitudes (or depths) and duration of the sag. Voltage sags cause speed variations on SM (with possible lost of synchronism), current and torque peaks and hence may cause tripping and equipment damage, which leads to financial losses. Three machines of different nominal power have been modeled and simulated with MATLAB in order to study its behavior under voltage sags. These SM's have been analyzed operating as generator, as motor, and in both cases, working under-excited and overexcited.